Two decompositions of the Pietra index with applications to Italian professional football teams

Two innovative procedures for the decomposition of the Pietra inequality index are proposed. Both are based on a two-step approach, already successfully applied in the literature to decompose other indexes. The first procedure allows the decomposition of the index by sources, while the second one provides the decomposition by subpopulations. A very important advantage of these two new procedures is that the first one allows to assess the relevance of each source, while the second one provides the contribution due to each subpopulation. The ”classical” decomposition of the Pietra index in the Within and the Between components can be easily obtained as a special case of the proposed decomposition procedure by subpopulations. Beyond the methodological details, two applications with real data regarding the professional football teams in Italy are illustrated.